CN110879040B - Displacement measurement method of Michelson heterodyne interferometer based on double acousto-optic modulator - Google Patents

Displacement measurement method of Michelson heterodyne interferometer based on double acousto-optic modulator Download PDF

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CN110879040B
CN110879040B CN201910886293.0A CN201910886293A CN110879040B CN 110879040 B CN110879040 B CN 110879040B CN 201910886293 A CN201910886293 A CN 201910886293A CN 110879040 B CN110879040 B CN 110879040B
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赵冬娥
马亚云
李沅
王思育
李诺伦
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North University of China
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
    • G01B11/02—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B9/00—Measuring instruments characterised by the use of optical techniques
    • G01B9/02—Interferometers
    • G01B9/02001—Interferometers characterised by controlling or generating intrinsic radiation properties
    • G01B9/02007—Two or more frequencies or sources used for interferometric measurement
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B9/00—Measuring instruments characterised by the use of optical techniques
    • G01B9/02—Interferometers
    • G01B9/02001—Interferometers characterised by controlling or generating intrinsic radiation properties
    • G01B9/0201—Interferometers characterised by controlling or generating intrinsic radiation properties using temporal phase variation
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B9/00—Measuring instruments characterised by the use of optical techniques
    • G01B9/02—Interferometers
    • G01B9/02015—Interferometers characterised by the beam path configuration
    • G01B9/02027—Two or more interferometric channels or interferometers
    • G01B9/02028—Two or more reference or object arms in one interferometer

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Abstract

The invention discloses a Michelson heterodyne interference nanometer displacement measurement method based on double acousto-optic modulators, which adopts a Michelson interference structure, and two arms are respectively added with an acousto-optic modulator to generate frequency shift; converting the first-order interference light spot into an electric signal through a one-dimensional detector, comparing the electric signal with a reference signal generated by a signal generator by using a phase lock device to obtain the phase difference between the first-order interference light spot and the reference signal, when the object generates nano displacement, the first-order diffraction light spot of the signal light carries the variation of the first-order diffraction light spot, the phase difference between the first-order interference signal containing the variation and the reference signal is changed, calculating the variation of the phase difference to obtain the phase variation caused by the nano displacement, and obtaining the displacement according to a phase difference and displacement formula; the system has simple optical path and easy adjustment, can effectively solve the problems of complex optical path, difficult adjustment and the like in the external interference in the prior art, and has obvious technical advantages in the fields of ultra-precise displacement and vibration measurement.

Description

Displacement measurement method of Michelson heterodyne interferometer based on double acousto-optic modulator
Technical Field
The invention belongs to the technical field of laser interferometry, and particularly relates to a displacement measurement method of a Michelson heterodyne interferometer based on double acousto-optic modulators.
Background
The laser heterodyne interferometer can overcome direct current drift caused by light intensity fluctuation, reduce laser power noise, can perform stable interferometric measurement in the measurement process, and has very high measurement resolution, so that the optical heterodyne interferometer becomes an instrument widely applied to precision measurement. In fact, the laser heterodyne interferometer is an improvement made on the basis of the michelson interferometer, and heterodyne interference can be realized by a double-frequency laser, and also by frequency shift devices such as an acousto-optic modulator (AOM) and electro-optic modulation. In many high-precision measurement systems, such as direction-identifiable high-precision doppler velocimeters, nanoscale heterodyne interferometers, doppler vibrometers, etc., a double-AOM heterodyne detection mode is usually adopted, AOMs with different frequency shift amounts are respectively added to two optical paths, and the mode has the advantages of low requirement on photoelectric receiver frequency response, high signal-to-noise ratio, easiness in matching optical paths, etc. The laser heterodyne interferometry has high resolution, a large measurement range and high system anti-interference capability, can be used for non-contact measurement, and is widely applied to the fields of displacement, angle and the like.
Heterodyne interferometry requires that a certain frequency difference be formed between two interference arms. The method for generating the frequency difference mainly utilizes the Zeeman effect and acousto-optic modulation. The Zeeman effect is affected by the frequency difference locking phenomenon, the generated double-frequency difference is generally small, and the maximum frequency difference does not exceed 4 MHz. The frequency difference obtained by the acousto-optic modulation method is usually large, the frequency difference reaches more than 20MHz, the frequency stability is very good, and the requirements of high-speed and high-precision measurement can be met.
At present, most heterodyne interference systems designed by using an acousto-optic modulator use Mach-Zehnder interference optical paths, but because a first-order light spot and a zero-order light spot generated by diffraction under the action of acousto-optic modulation have a certain angle, the interference optical path has a complex structure and is difficult to adjust.
Disclosure of Invention
In view of this, the present invention aims to provide a displacement measurement method for a michelson heterodyne interferometer based on a dual acousto-optic modulator, which can measure nanoscale displacement and effectively solve the problem of difficult optical path adjustment.
A displacement measurement method is based on a Michelson interferometer, and an acousto-optic modulator is respectively arranged on a reference arm and a signal arm of the Michelson interferometer; the displacement measurement method comprises the following steps:
step 1, under the condition that two acousto-optic modulators do not work, the reference light and the signal light which are finally emergent generate interference by adjusting the arm lengths of a reference arm and a signal arm;
step 2, respectively adjusting the angles of the two acousto-optic modulators relative to the laser beam on the optical path under the working state of the two acousto-optic modulators, so that the laser beam only generates a zero-order beam and a first-order beam after acousto-optic diffraction;
step 3, respectively inputting frequency f to the two acousto-optic modulators1、f2The sinusoidal signal drives the two acousto-optic modulators to work; is connected withReceiving the first-order diffraction beam of the reference light and the first-order diffraction beam of the signal light, and obtaining interference signals of the first-order diffraction beam of the reference light and the first-order diffraction beam of the signal light, wherein the interference signals are defined as first-order interference signals and are expressed as follows:
Figure BDA0002207389350000021
wherein A is the amplitude of the first-order interference signal,
Figure BDA0002207389350000022
is the initial phase of the first order interference signal; f ═ f1-f2；
Step 4, generating a sinusoidal signal with the frequency f ═ Δ f as a reference signal, wherein the signal expression is as follows:
Figure BDA0002207389350000023
wherein B is the amplitude of the reference signal,
Figure BDA0002207389350000024
is the phase of the reference signal;
step 5, obtaining the phase difference between the primary interference signal and the reference signal
Figure BDA0002207389350000025
Step 6, after the measured object generates displacement, obtaining the initial phase of the first-order interference signal of the reference light and the signal light, and using
Figure BDA0002207389350000026
Indicating that the phase difference between the first-order interference spot signal and the reference signal is present
Figure BDA0002207389350000027
Step 7, obtaining the phase difference before and after the displacement of the measured object
Figure BDA0002207389350000031
Figure BDA0002207389350000032
According to phase and displacement
Figure BDA0002207389350000033
The displacement variation Δ z is obtained from the relational expression (1).
Preferably, the two acousto-optic modulators are respectively arranged on a rotary table, and the angle of the two acousto-optic modulators relative to the laser beam of the located light path is adjusted by rotating the rotary table.
Preferably, the two-dimensional photoelectric sensor is used for receiving the reference light and the signal light which are finally emitted, and whether interference is generated or not is judged by observing an image on the two-dimensional photoelectric sensor.
Preferably, the signal generator is used to generate the frequency f1、f2Of the sinusoidal signal.
Preferably, a one-dimensional photodetector is used to receive the first-order interference signal.
Preferably, the first-order interference signal is input to a signal input end of the phase locker, and the reference signal is input to a reference input end of the phase locker; and calculating the phase difference between the primary interference signal and the reference signal through the phase lock.
Preferably, the piezoelectric ceramic is used for controlling the object to be measured to generate nano-scale displacement.
The invention has the following beneficial effects:
the invention discloses a Michelson heterodyne interference nanometer displacement measurement method based on double acousto-optic modulators, which adopts a Michelson interference structure, two arms are respectively added with an acousto-optic modulation device to generate frequency shift, the driving frequencies of the two acousto-optic modulators in a system are different, and two first-order diffracted light beams with different frequencies are generated, so that heterodyne interference is formed; converting the first-order interference light spot into an electric signal through a one-dimensional detector, comparing the electric signal with a reference signal generated by a signal generator by using a phase lock device to obtain the phase difference between the first-order interference light spot and the reference signal, when the object generates nano displacement, the first-order diffraction light spot of the signal light carries the variation of the first-order diffraction light spot, the phase difference between the first-order interference signal containing the variation and the reference signal is changed, calculating the variation of the phase difference to obtain the phase variation caused by the nano displacement, and obtaining the displacement according to a phase difference and displacement formula; the system has simple optical path and easy adjustment, can effectively solve the problems of complex optical path, difficult adjustment and the like in the external interference in the prior art, and has obvious technical advantages in the fields of ultra-precise displacement and vibration measurement.
Drawings
FIG. 1 is a schematic diagram of a light path of a nanometer displacement measurement system of a Michelson heterodyne interferometer based on a double acousto-optic modulator according to the present invention;
FIG. 2 is a graph of signal versus time for a reference signal and a reference signal received before a shift in simulation;
fig. 3 is a graph of the signal versus time of a reference signal and a reference signal received after a shift in simulation.
The system comprises a laser 1, a beam splitter 2, a first acousto-optic modulator 3, a second acousto-optic modulator 4, a first standard reflector 5, a second standard reflector 6 and a total reflection right-angle prism 7, wherein the laser is connected with the beam splitter 2; 8-two-dimensional photoelectric sensor, 9-one-dimensional photoelectric sensor.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
The invention aims to solve the problems of difficult adjustment of an optical path, nonlinear error and the like of the conventional Mach-Zehnder laser heterodyne interference optical path structure and principle, and discloses a double-acousto-optic modulator-based Michelson heterodyne interference nanometer displacement measurement system.
As shown in fig. 1, a michelson heterodyne interference position-shifting system based on a double acousto-optic modulator, a conventional michelson interferometer includes a laser light source 1, a beam splitter prism 2, a first standard reflector 5, a second standard reflector 6, a measured object, and a two-dimensional photoelectric sensor 8; the second standard reflector 6 is fixed on the measured object and used for returning the light path; the object to be measured generates displacement through the piezoelectric ceramics.
The laser light source 1 is used for outputting a laser beam; the beam splitter prism 2 is used for splitting the laser beam into two paths, the reflected beam is used as a reference beam, and the transmitted beam is used as a measuring beam; the reference beam returned by the first standard reflector 5 is transmitted to the two-dimensional photoelectric sensor 8 through the beam splitter prism 2, the measuring beam reflected by the second standard reflector 6 enters the two-dimensional photoelectric sensor 8 after being reflected by the beam splitter prism 2, the measuring beam and the reference beam are combined into one beam, an interference fringe two-dimensional photoelectric sensor 8 is generated on the two-dimensional photoelectric sensor 8, and a zero-order beam interference fringe is received;
on the basis of the Michelson interferometer, an acousto-optic modulator (the distances from the two acousto-optic modulators to a beam splitter prism 2 are equal) is added in a reference arm and a measuring arm respectively; a total reflection right-angle prism 7 and a one-dimensional photoelectric detector 9 are added to form the Michelson heterodyne interferometer based on the double acousto-optic modulator;
the two acousto-optic modulation devices are used for generating different frequency shifts for the two paths of laser beams; the laser light source 1 is divided into reference light and signal light after being split by the splitting prism 2, the reference light reaches the reflector 5 after passing through the acousto-optic modulator 3, and the light beam reflected by the reflector 5 passes through the acousto-optic modulator 3 again to generate a multi-stage diffracted light beam of the reference light under the action of acousto-optic diffraction; after the zero-order light beam and the first-order light beam of the reference light are transmitted by the beam splitter prism 2, the zero-order light beam is imaged on the two-dimensional photoelectric detector 8, and the first-order light beam reaches the one-dimensional photoelectric detector 9 through the total reflection right-angle prism 7.
The signal light reaches the reflector 6 through the acousto-optic modulator 4, and can generate a multi-stage diffracted light beam under the acousto-optic diffraction action of the acousto-optic modulator 4 after being reflected by the reflector 6; in the invention, in order to ensure the precision of displacement measurement, the angle between the acousto-optic modulator 4 and the laser beam is adjusted, so that the laser beam after acousto-optic diffraction only generates a zero-order beam and a first-order beam, the zero-order beam and the first-order beam of the signal light are reflected by the beam splitter prism 2, the zero-order beam is imaged on the two-dimensional photoelectric sensor 8, and the first-order beam is reflected by the total reflection prism 7 to reach the one-dimensional detector 9.
The zero-order light beams of the reference light and the signal light generate interference fringes of a zero-order light spot on the two-dimensional photoelectric detector 8, and the first-order light beam generates a first-order interference light spot on the one-dimensional photoelectric detector 9.
The two acousto-optic modulators are respectively arranged on a rotary table, and when the rotary table is rotated, the diffracted light beams only have zero-order light beams and first-order light beams, and the light intensities of the zero-order light beams and the first-order light beams are equal, the light intensities reach the Bragg diffraction angle, and the rotary table is locked.
Based on the principle, the displacement measuring method comprises the following steps:
step 1, in the state that two acousto-optic modulators do not work, two paths of zero-order light beams generate interference fringes on a two-dimensional photoelectric sensor 8 by adjusting the optical path difference of reference light and signal light;
step 2, respectively adjusting the angles of the two acousto-optic modulators relative to the laser beam on the optical path under the working state of the two acousto-optic modulators, and modulating and diffracting the acousto-optic modulators into first-order diffraction, namely, the laser beam only generates a zero-order beam and a first-order beam after acousto-optic diffraction; in step 1, the zero-order fringe has reached the interference condition, and when the first-order diffracted light of the reference light and the signal light comes out from the beam splitter prism, the interference state of the first-order diffracted light beams can be reached.
Step 3, outputting the same amplitude by using a signal generator, wherein the frequencies are respectively f1、f2Of (d) is a sinusoidal signal (f)1And f2The frequency difference between the two is required to be within the receiving range of the detector), two acousto-optic modulators are respectively driven to work, and under the action of acousto-optic modulation, the frequency of the first-order diffracted beam of the reference light is increased by f on the frequency of the light per se1The frequency of the first-order diffracted beam of the signal light is increased by f2. Thus, the first order diffraction light spot of the signal light and the reference light interfere to generate a difference frequency signal of delta f-f1-f2。
The expression of the first order diffracted beam of the reference light is E1＝A1cos[2π(f0+f1)t]
A1Representing the first order diffraction of the reference lightAmplitude of the light beam, f0Representing the frequency of light, f1The frequency shift amount of the acousto-optic modulator of the reference light path is shown, and t represents time.
The expression of the first order diffracted beam of the test light is E2＝A2cos[2π(f0+f2)t]
A2Representing the amplitude, f, of the first-order diffracted beam of the signal light2Representing the amount of frequency shift of the signal path acousto-optic modulator.
The first order diffracted beam interference expression of the reference light and the signal light is as follows:
Figure BDA0002207389350000061
since the photodetector cannot respond to high-frequency light (beyond the frequency response range), the light intensity received by the photodetector is expressed as:
Figure BDA0002207389350000071
the one-dimensional photodetector 9 receives the first-order interference light spot of the reference light and the signal light, converts the light signal into an electrical signal, and simultaneously adds a capacitor to filter out a direct current quantity, so that the expression is as follows:
Figure BDA0002207389350000072
wherein A is the amplitude of the signal,
Figure BDA0002207389350000073
an initial phase of a primary interference signal of the reference light and the signal light;
step 4, inputting the interference signal received by the one-dimensional photoelectric detector 9 into the signal input end of the phase-locked loop;
and step 5, setting a sinusoidal signal with the output frequency f ═ Δ f of the signal generator as a reference signal, wherein the signal expression is as follows:
Figure BDA0002207389350000074
whereinAnd B is the amplitude of the reference signal,
Figure BDA0002207389350000075
is the phase of the reference signal; inputting the reference signal into a reference input end of a phase locker;
step 6, performing phase-locked amplification calculation on the input interference signal and the reference signal by using a phase lock device to obtain the phase difference between the first-level interference light spot signal and the reference signal
Figure BDA0002207389350000076
This is the situation before the object to be measured is displaced.
And 7, when the piezoelectric ceramic generates nano displacement, according to the method from the step 4 to the step 6, as the object to be measured is displaced, the initial phase of the first-order interference signal of the reference light and the signal light is changed, and the method is used
Figure BDA0002207389350000077
Indicating that the phase difference between the first-order interference spot signal and the reference signal is present
Figure BDA0002207389350000078
Step 8, obtaining the phase difference before and after the displacement of the measured object
Figure BDA0002207389350000079
Figure BDA00022073893500000710
According to phase and displacement
Figure BDA00022073893500000711
The displacement variation Δ z is obtained from the relational expression (1).
In this embodiment, the splitting ratio of the splitting prism 2 is 50: 50.
in summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (7)

1. A displacement measurement method is based on a Michelson interferometer and is characterized in that an acousto-optic modulator is respectively arranged on a reference arm and a signal arm of the Michelson interferometer; the displacement measurement method comprises the following steps:
step 1, under the condition that two acousto-optic modulators do not work, the reference light and the signal light which are finally emergent generate interference by adjusting the arm lengths of a reference arm and a signal arm;
the Michelson interferometer comprises a laser light source (1), a beam splitter prism (2), a first standard reflector (5), a second standard reflector (6), a two-dimensional photoelectric sensor (8), a total reflection right-angle prism (7) and a one-dimensional photoelectric detector (9); the second standard reflector (6) is fixed on the measured object and used for returning the light path; the object to be measured generates displacement through the piezoelectric ceramics;
the laser light source (1) is used for outputting a laser beam; the beam splitter prism (2) is used for splitting the laser beam into two paths, the reflected beam is used as a reference beam, and the transmitted beam is used as a measuring beam; the reference light beam returned by the first standard reflector (5) is transmitted to the two-dimensional photoelectric sensor (8) through the beam splitter prism (2), the measuring light beam reflected by the second standard reflector (6) enters the two-dimensional photoelectric sensor (8) after being reflected by the beam splitter prism (2), the measuring light beam and the reference light beam are combined into one beam, interference fringes are generated on the two-dimensional photoelectric sensor (8), and the two-dimensional photoelectric sensor (8) receives the zero-order light beam interference fringes;
the two acousto-optic modulation devices are used for generating different frequency shifts for the two paths of laser beams; the laser light source (1) is divided into reference light and signal light after being split by the splitting prism (2), the reference light reaches the first standard reflector (5) after passing through the acousto-optic modulator (3), and light beams reflected by the first standard reflector (5) pass through the acousto-optic modulator (3) again; after the zero-order light beam and the first-order light beam of the reference light are transmitted by the beam splitter prism (2), the zero-order light beam is imaged on a two-dimensional photoelectric sensor (8), and the first-order light beam reaches a one-dimensional photoelectric detector (9) through a total reflection right-angle prism (7);
the signal light reaches a second standard reflector (6) through an acousto-optic modulator (4), after being reflected by the second standard reflector (6), a zero-order light beam and a first-order light beam are generated under the acousto-optic diffraction action of the acousto-optic modulator (4), after being reflected by a beam splitter prism (2), the zero-order light beam is imaged on a two-dimensional photoelectric sensor (8), and the first-order light beam is reflected by a total reflection right-angle prism (7) to reach a one-dimensional photoelectric detector (9);
interference fringes of zero-order light spots are generated on a two-dimensional photoelectric sensor (8) by zero-order light beams of the reference light and the signal light, and first-order light spots are generated on a one-dimensional photoelectric detector (9) by first-order light beams;
step 2, respectively adjusting the angles of the two acousto-optic modulators relative to the laser beam on the optical path under the working state of the two acousto-optic modulators, so that the laser beam only generates a zero-order beam and a first-order beam after acousto-optic diffraction;
step 3, respectively inputting frequency f to the two acousto-optic modulators1、f2The sinusoidal signal drives the two acousto-optic modulators to work; receiving the first-order diffracted beam of the reference light and the first-order diffracted beam of the signal light, and obtaining an interference signal of the first-order diffracted beam of the reference light and the first-order diffracted beam of the signal light, which is defined as a first-order interference signal and expressed as:
Figure FDA0003428522140000021
wherein A is the amplitude of the first-order interference signal,
Figure FDA0003428522140000022
is the initial phase of the first order interference signal; f ═ f1-f2；
Step 4, generating a sinusoidal signal with the frequency f ═ Δ f as a reference signal, wherein the signal expression is as follows:
Figure FDA0003428522140000023
wherein B is the amplitude of the reference signal,
Figure FDA0003428522140000024
is the phase of the reference signal;
step 5, obtain onePhase difference of stage interference signal and reference signal
Figure FDA0003428522140000025
Step 6, after the measured object generates displacement, obtaining the initial phase of the first-order interference signal of the reference light and the signal light, and using
Figure FDA0003428522140000026
Indicating that the phase difference between the first-order interference spot signal and the reference signal is present
Figure FDA0003428522140000027
Step 7, obtaining the phase difference before and after the displacement of the measured object
Figure FDA0003428522140000028
Figure FDA0003428522140000029
According to phase and displacement
Figure FDA00034285221400000210
The displacement variation Δ z is obtained from the relational expression (1).
2. A displacement measuring method according to claim 1, wherein two acousto-optic modulators are respectively disposed on a rotary table, and the angles of the two acousto-optic modulators with respect to the laser beam in the optical path are adjusted by rotating the rotary table.
3. A displacement measuring method according to claim 1, wherein the reference light and the signal light which are finally emitted are received by a two-dimensional photosensor, and whether or not interference occurs is judged by observing an image thereon.
4. A displacement measuring method according to claim 1, characterized in that signals are usedThe generator generates a frequency f1、f2Of the sinusoidal signal.
5. A displacement measuring method according to claim 1, wherein the primary interference signal is received by a one-dimensional photodetector.
6. A displacement measuring method according to claim 1, wherein the primary interference signal is input to a signal input terminal of the phase-locked loop, and the reference signal is input to a reference input terminal of the phase-locked loop; and calculating the phase difference between the primary interference signal and the reference signal through the phase lock.
7. A displacement measuring method according to claim 1, wherein the object to be measured is controlled to produce nano-scale displacement by using a piezoelectric ceramic.
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